I'm also relying on perlmonks in order to find examples, which are commented, corrected,..
However, having these examples in the docs would be a big advantage, finally the docs should be there for not having the need of any further documentation sources.

I like the approach of some module authors, who create a examples subdir in their module distribution. (Although I always have to digg into my ~/.cpan/..)

That's how I try to get familiar with new modules (and also programming languages):

Separate the problem to solve of the rest of the program

Write a small script

Try to get examples, copy them into the script, replace the names, extend the examples

Play around with the script, until I've got a good feeling/the script does what it's supposed to do...

Although that's sort of copy and paste programming, I'm able to get familiar with new modules quite fast this way.
I'd think the important point is the playing with the script..

I should also remark that I've got some directories which contain such small scripts.
This way I'm able to remember and reuse solutions I already figured out.